Finite Group Databasebeta

← #14642247

Subgroups — #14642247

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076968C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3#13066440C214yesmaximal, complemented
4C11×#1728C211yesmaximal, characteristic
5C22×C11×M16—21no—
6C22×C42×C11C2211yescharacteristic
7C2×#66977—21no—
8C2×#66922C411yescharacteristic
9#10622825—21no—
10#10622825C412yes—
11C2×C22⋊(C11⋊C8)—21no—
12#10622548C411yescharacteristic
13#10622542—21no—
14#10622541—21no—
15#10622541C2212yes—
16C2×C4×C11⋊C8—21no—
17C11×#336—21no—
18C11×#336C2212yes—
19#10622162C2212yes—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C22×Dic22—21no—
24C2×C11×M16—24no—
25C2×C11×M16—42no—
26C2×C11×M16—42no—
27C22×C8×C11—22no—
28C2×C42×C11—42no—
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C22⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C412yes—
38C2×C4⋊Dic11C2×C412yes—
39#66977—42no—
40#66977—42no—
41C2×Dic11⋊C4—22no—
42C22×C11⋊C8—22no—
43#66922—42no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C22⋊(C11⋊C8)—24no—
47C4×C11⋊C8—42no—
48#7685—111nomaximal, Sylow
49C24×C11C22⋊C411yescharacteristic
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11D812yes—
62C22×C4×C11SD1612yes—
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—22no—
67C22×Dic11—22no—
68C2×Dic22—42no—
69C2×Dic22—42no—
70C2×Dic22—42no—
71C11×M16—48no—
72C2×C8×C11—24no—
73C2×C8×C11—42no—
74C2×C8×C11—42no—
75C42×C11—22no—
76C42×C11—22no—
77C42×C11—41no—
78C42×C11—41no—
79C22⋊Dic11—44no—
80C4⋊Dic11—24no—
81C4⋊Dic11—42no—
82C4⋊Dic11—42no—
83C4⋊Dic11—42no—
84C4⋊Dic11—42no—
85Dic11⋊C4—42no—
86Dic11⋊C4—42no—
87C2×C11⋊C8—24no—
88C2×C11⋊C8—42no—
89C2×C11⋊C8—42no—
90#2857—111no—
91C4×C22⋊C8—111no—
92#1728D1111yescharacteristic
93#1271—114no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11#10212yes—
101C23×C11C2×C22⋊C411yescharacteristic
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—24no—
113C2×C4×C11—24no—
114C2×C4×C11—44no—
115C2×C4×C11—44no—
116C2×C4×C11#9912yes—
117C2×C4×C11#10112yes—
118C2×C4×C11#10212yes—
119C2×C4×C11#10412yes—
120C2×C4×C11#10412yes—
121C2×C4×C11#13112yes—
122C2×C4×C11C2×D811yescharacteristic
123C2×C4×C11C2×SD1611yescharacteristic
124C2×C4×C11#13712yes—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131Dic22—84no—
132C8×C11—44no—
133C11⋊C8—44no—
134C22×M16—21no—
135C2×C4⋊Q8—111no—
136C2×C22⋊Q8—221no—
137C22×C42C2×D1111yescharacteristic
138C2×C22⋊C8—221no—
139C2×C4×C8—221no—
140#391—221no—
141#389—112no—
142#389—221no—
143#384—111no—
144#380—112no—
145#380—221no—
146#336—21no—
147#336—112no—
148#336C2×D1112yes—
149C22×C11—22no—
150C22×C11—22no—
151C22×C11—22no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11#40811yescharacteristic
157C22×C11C2×#9911yescharacteristic
158C22×C11C2×#10111yescharacteristic
159C22×C11C2×#10211yescharacteristic
160C22×C11#41911yescharacteristic
161C22×C11C2×#10411yescharacteristic
162C22×C11C2×#10411yescharacteristic
163C4×C11—22no—
164C4×C11—22no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—22no—
168C4×C11—22no—
169C4×C11#32714yes—
170Dic11—82no—
171Dic11—82no—
172C22×Q8—221no—
173C23×C4C4×D1111yescharacteristic
174C23×C4D4411yescharacteristic
175C23×C4C22⋊D1111yescharacteristic
176C2×M16—24no—
177C2×M16—42no—
178C2×M16—42no—
179C22×C8—22no—
180C22×C8—222no—
181C4⋊Q8—442no—
182C22⋊Q8—442no—
183C22⋊Q8—442no—
184C2×C4⋊C4—112no—
185C2×C4⋊C4—112no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—222no—
190C2×C22⋊C4—222no—
191C2×C42—42no—
192C2×C42C4×D1111yescharacteristic
193C2×C42D4411yescharacteristic
194C2×C42C22⋊D1111yescharacteristic
195C2×C42C22×D1111yescharacteristic
196C22⋊C8—224no—
197C4×C8—442no—
198#95—222no—
199#95—222no—
200C2×C11—42no—
201C2×C11#147211yescharacteristic
202C2×C11#148511yescharacteristic
203C2×C11#149211yescharacteristic
204C2×C11C2×#32711yescharacteristic
205C2×C11#150811yescharacteristic
206C2×C11#152611yescharacteristic
207C2×C11#154611yescharacteristic
208C24(C2×D11)⋊C411yescharacteristic
209C2×Q8—442no—
210C2×Q8—442no—
211C2×Q8—442no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—222no—
221C22×C4—222no—
222C22×C4(C2×D11)⋊C411yescharacteristic
223C22×C4(C2×D11)⋊C411yescharacteristic
224C22×C4(C2×D11)⋊C411yescharacteristic
225C22×C4#432312yes—
226C22×C4#432512yes—
227C22×C4C2×C4×D1111yescharacteristic
228C22×C4C2×D4411yescharacteristic
229C22×C4C2×C22⋊D1111yescharacteristic
230M16—48no—
231C2×C8—24no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—224no—
235C2×C8—442no—
236C2×C8—442no—
237C4⋊C4—224no—
238C4⋊C4—442no—
239C4⋊C4—442no—
240C4⋊C4—442no—
241C4⋊C4—442no—
242C4⋊C4—442no—
243C4⋊C4—442no—
244C22⋊C4—444no—
245C42—22no—
246C42—22no—
247C42—41no—
248C42—41no—
249C11#768511yescharacteristic, complemented, Sylow
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23#6687312yes—
257C23C2×(C2×D11)⋊C411yescharacteristic
258Q8—884no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—442no—
274C2×C4—442no—
275C2×C4—442no—
276C2×C4—442no—
277C2×C4—442no—
278C2×C4—442no—
279C2×C4#6686912yes—
280C2×C4#6687012yes—
281C2×C4#6687312yes—
282C2×C4#6688812yes—
283C2×C4#6688912yes—
284C2×C4#6696012yes—
285C2×C4#6696212yes—
286C2×C4C2×#432311yescharacteristic
287C2×C4C2×#432511yescharacteristic
288C8—44no—
289C8—444no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C2×#6686911yescharacteristic
298C22C2×#6687011yescharacteristic
299C22C2×#6687311yescharacteristic
300C22#1062273311yescharacteristic
301C22#1062274211yescharacteristic
302C22C2×#6688811yescharacteristic
303C22C2×#6688911yescharacteristic
304C4—21no—
305C4—21no—
306C4—22no—
307C4—22no—
308C4—22no—
309C4—22no—
310C4—882no—
311C4—882no—
312C4#1062208914yes—
313C2—42no—
314C2#1306698111yescharacteristic
315C2#1306703811yescharacteristic
316C2#1306706611yescharacteristic
317C2C2×#1062208911yescharacteristic
318C2#1306713711yescharacteristic
319C2#1306721011yescharacteristic
320C2#1306728911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1728C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1728D11
hypocenterC11#7685
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1728

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13066440C2semidirect
249. C11#7685semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130769682
C4×C22⋊(C11⋊C8)2
#130664402
C11×#17282
#768511